MWIV
4.6 Curie Temperature Measurement
4.7.3 Techniques of Measurements of Permeability
Measurements of permeability normally involve the measurements of the change in self-inductance of a coil in presence of the magnetic core. The behavior of a self-inductance can now be described as follows. Suppose we have an ideal lossless air coil of inductance L0. On insertion of magnetic core with permeability
t, the inductance will be jiL0. The complex impedance Z of this coil can be expressed as
Z= R+jX =jo)L011 =jwLo(ji'-jjf) (4.17)
where the resistive part is
R=oL0 ji' (4.18)
and the reactive part is
X=oL0g' (4.19)
The radio frequency (RF) permeability can be derived from the complex impedance of a coil Z (equation 4.17). The core is usually toroidal to avoid demagnetizating effects. The quantity L0 is derived geometrically.
4.7.4 Frequency Characteristics of Ferrite Samples
The frequency characteristics of the hexaferrite samples i.e. the permeability spectra were investigated using a Hewlett Packard Impedance Analyzer of model No. 4192A. The measurements of inductances were taken in the frequency range of I kHz to 13MHz. The values of measured parameters obtained as a function of
Chapter Four Experimental Details
frequency and the real and imaginary part of permeability and the loss factor are calculated. p.' is calculated by using the following formula
(4.20)
andtan6=— (4.21)
/1
Where L is the self-inductance of the sample core
and L0 = (4.22)
where L0 is the inductance of the winding coil without the sample core and N is the number of turns of coil (here N5), s is the area of cross section as given below and N is the number of turns of coil (here N5), s is the area of cross section as given below s=dh, where, d=(d1-d2)/2, h=height
and
J
is the mean diameter of the sample given as follows: - = d1 + d24.8 Resistivity Measurement
Resistivity is an intrinsic property of a magnetic material. Ferrites materials are technically very important because of their high resistivity and low eddy current losses. Eddy current losses are inversely proportional to resistivity of the ferrite samples. Therefore, the measurement of resistivity is very crucial for the ferrite materials.
For the resistivity measurement the samples were sintered at 1245°C for 2 hours in air. The samples were polished using metallurgical polishing machine with the help of silicon carbide MRE papers with grid size 600, 800 and 1200 successively.
After that the samples were clean with acetone and then again polished with special velvet type polishing cloth named as alphagarn for finer polishing using fine alumina powder dispersed in a liquid. Samples are then cleaned in a ultrasonic cleaner and dried in furnace at 150°C for several hours. Then the samples are again cleaned with acetone and silver paste was added to both the sides of the
Chapter Four Experimental Details
polished pellet samples together with two thin copper wires of 100-micron diameter for conduction. Again the samples are dried at 150°C to eliminate any absorbed moisture. DC resistivity was measured using an electrometer Keithley model 6514, USA at room temperature. The resistivity has been calculated using the formula,
p = R A
ohm-meter (4.23)
Where 1 is the length and A is the cross-sectional area of the samples. The conduction electrons are responsible for the current flow. The electron undergoes a collision only because the lattice is not perfectly regular. We group the derivations from a perfect lattice into two classes: lattice vibrations (phonons) of the ions around their equilibrium position due to thermal excitation of the ions and all static imperfections, such as foreign impurities or crystal defects. Now we can write
PPph +Pt (4.24)
It is seen that p has split into two terms: a term p, is due to scattering by impurities, which is independent of T, called residual resistivity. Another term added to this is Pph arises from the scattering by phonons and therefore temperature dependent. This is called ideal resistivity.
At low temperature T, the scattering by phonons is negligible because the amplitudes of oscillations are very small; in that region Pph _> 0, is a constant. As T increases, scattering by phonons becomes more effective and Pph (T) increases;
this is why p increases. When T becomes significantly large, scattering by phonons dominates and p p 1 (T). In the high temperature region Pph (T) increases linearly with T. Resistivity linearly increases with T up to the melting point for the case of pure element. On the other hand, the electrical resistivity of metallic glass is measured to be very high due to the disorder arrangement of the atoms. The electrons suffer enormous scattering as they pass through the disorder matrix of ions. Thus the mean free paths of the conduction electrons are very short
Chapter Four Experimental Details
and hence the drift velocities of the electrons are very low giving the material a property of high electrical resistivity. This resistivity may drop quite abruptly at a certain temperature as the temperature of the sample is increased. The increase in temperature give rise to the information of small regions of ordered phases at the onset of segregation and thus attaining the crystalline phase when the resistivity falls simply as the crystallization temperature. This unique property of the metallic glass is of very interesting of the people who are working with the commercial applications of metallic glasses e.g., the power supplies, transformers, magnetic heads, magnetic shielding etc. Ferrites are semiconductors, and their resistivity decreases with increasing temperature according to the relation:
p=p0e K;T (4.25)
The temperature dependence of chemical reactions can be expressed by defining the activation energy
E0=K8T2 dlnp (4.26)
dT
By using d () = - and rearranging equation (4.32) we obtain
-
R d lnp
(4.27)
d (—)
Ea is the energy needed to release an electron from the ion for a jump to the neighboring ion giving rise to electrical conductivity known as the activation energy [4.5-4.6].